$A$ $B$ $C$ If: $ AC = 53$, $ BC = 2x + 5$, and $ AB = 4x + 6$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 6} + {2x + 5} = {53}$ Combine like terms: $ 6x + 11 = {53}$ Subtract $11$ from both sides: $ 6x = 42$ Divide both sides by $6$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $BC$ $ BC = 2({7}) + 5$ Simplify: $ {BC = 14 + 5}$ Simplify to find ${BC}$ : $ {BC = 19}$